Problem: Factor completely. $5x^2+20x-60=$
Explanation: First, let's factor out the greatest common factor. If the leading coefficient is negative, we'll also factor out $-1$. The result will be something like this, where the blanks are coefficients: $_{\llcorner\!\lrcorner}\!(_{\llcorner\!\lrcorner}\! x^2+\, _{\llcorner\!\lrcorner}\! x+\, _{\llcorner\!\lrcorner}\!)$ Then, we can try to factor the sum like this: $_{\llcorner\!\lrcorner}\!(_{\llcorner\!\lrcorner}\! x+\, _{\llcorner\!\lrcorner}\!) (_{\llcorner\!\lrcorner}\! x+\, _{\llcorner\!\lrcorner}\!)$ Factor out a the greatest common factor The greatest common factor is $5$. $\begin{aligned} &\phantom{=}5x^2+20x-60 \\\\ &=5(x^2+4x-12) \end{aligned}$ [How did we find the greatest common factor?] Factor $x^2+4x-12$ $\begin{aligned} &\phantom{=}5x^2+20x-60 \\\\ &=5(x^2+4x-12) \\\\ &=5(x-2)(x+6) \end{aligned}$ [I want to see this step in more detail.] Answer $\begin{aligned} &\phantom{=}5x^2+20x-60 \\\\ &=5(x-2)(x+6) \end{aligned}$